A tire manufacturer is considering a newly designed tread pattern for its sports

Question

A tire manufacturer is considering a newly designed tread pattern for its sports tires. Tests indicate that these tires will provide better gas mileage and longer tread life. The company test the tires for braking effectiveness, hoping the tires will allow a car traveling at 60 mph to completely stop in 110 feet after the brakes are applied. They will adopt the new tread pattern unless there is strong evidence that the tires do not meet this objective.

Conduct a hypothesis test and give your recommendations.

a) With a P-value below 5% significance, we fail to reject the null hypothesis. The sample is evidence that the new tread pattern stops a car in 110 feet.

b) With a P-value below 5% significance, we reject the null hypothesis. The sample is evidence that the new tread pattern stops a car in 110 feet.

c) With a P-value below 5% significance, we reject the null hypothesis. The sample is evidence that the new tread pattern does not stop a car in 110 feet.

d) With a P-value above 5% significance, we reject the null hypothesis. The sample is evidence that the new tread pattern stops a car in 110 feet.

e) With a P-value above 5% significance, we fail to reject the null hypothesis. The sample is evidence that the new tread pattern does not stop a car in 110 feet.

Explanation / Answer

Given that,
population mean(u)=110
sample mean, x =107.9091
standard deviation, s =2.8091
number (n)=11
null, Ho: =110
alternate, H1: <110
level of significance, = 0.05
from standard normal table,left tailed t /2 =1.812
since our test is left-tailed
reject Ho, if to < -1.812
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =107.9091-110/(2.8091/sqrt(11))
to =-2.4687
| to | =2.4687
critical value
the value of |t | with n-1 = 10 d.f is 1.812
we got |to| =2.4687 & | t | =1.812
make decision
hence value of | to | > | t | and here we reject Ho
p-value :left tail - Ha : ( p < -2.4687 ) = 0.01659
hence value of p0.05 > 0.01659,here we reject Ho
ANSWERS
---------------
null, Ho: =110
alternate, H1: <110
test statistic: -2.4687
critical value: -1.812
decision: reject Ho
p-value: 0.01659

[ANSWER]
With a P-value below 5% significance, we reject the null hypothesis. The sample is evidence that the new tread pattern stops a car in 110 feet.

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